This is the polynomial of variable x whose degree is 4. So we can say that this equation must have four roots. One of the root is given that is -1+i.Since it is a complex number we can consider that another root as -1- i

So let us take α = -1 + i β = - 1 - i

By using these two roots we can find a quadratic equation which is the part of the original equation.First let us find the quadratic equation.

General form of any quadratic equation:

x² - (α + β) x + α β = 0

α = -1 + i β = - 1 - i

Sum of roots (α + β) = -1 + i - 1 - i

= - 2

Product of roots (α β) = (-1 + i) (- 1 - i)

= (-1)² - i²

= 1 - (-1)

= 1 + 1

= 2

Therefore the required quadratic equation

x² - (-2) x + 2 = 0

x² + 2 x + 2 = 0

This is the part of the equation of polynomial of degree 4.

By solving this quadratic equation x² + 2 x - 1 = 0 we can get other two roots. We can not factorize this quadratic equation. For solving this quadratic equation we have to use formula.